Resolution enhancement in medical ultrasound imaging

Abstract

Image resolution enhancement is a problem of considerable interest in all medical imaging modalities. Unlike general purpose imaging or video processing, for a very long time, medical image resolution enhancement has been based on optimization of the imaging devices. Although some recent works purport to deal with image postprocessing, much remains to be done regarding medical image enhancement via postprocessing, especially in ultrasound imaging. We face a resolution improvement issue in the case of medical ultrasound imaging. We propose to investigate this problem using multidimensional autoregressive (AR) models. Noting that the estimation of the envelope of an ultrasound radio frequency (RF) signal is very similar to the estimation of classical Fourier-based power spectrum estimation, we theoretically show that a domain change and a multidimensional AR model can be used to achieve super-resolution in ultrasound imaging provided the order is estimated correctly. Here, this is done by means of a technique that simultaneously estimates the order and the parameters of a multidimensional model using relevant regression matrix factorization. Doing so, the proposed method specifically fits ultrasound imaging and provides an estimated envelope. Moreover, an expression that links the theoretical image resolution to both the image acquisition features (such as the point spread function) and a postprocessing feature (the AR model) order is derived. The overall contribution of this work is threefold. First, it allows for automatic resolution improvement. Through a simple model and without any specific manual algorithmic parameter tuning, as is used in common methods, the proposed technique simply and exclusively uses the ultrasound RF signal as input and provides the improved B-mode as output. Second, it allows for the a priori prediction of the improvement in resolution via the knowledge of the parametric model order before actual processing. Finally, to achieve the previous goal, while classical parametric methods would first estimate the model order and then the model parameters, our approach estimates the model parameters and the order simultaneously. The effectiveness of the methodology is validated using two-dimensional synthetic and in vivo data. We show that, compared to other techniques, our method provides better results from a qualitative and a quantitative viewpoint.

Keywords: autoregressive; multidimensional processing; super-resolution; ultrasound.

Fig. 1

Principle of B-mode imaging. Like the original ultrasound image, which is a collection of $g(z)$ echoes, the B-mode image is a collection of B-mode echoes.

Fig. 2

Two-point sources.

Fig. 3

Signal-to-noise ratio (SNR) versus resolution and order for an ideal point spread function (PSF). The SNR goes from 25 dB at the top to $-30\mathrm{dB}$ for the bottom line.

Fig. 4

SNR versus resolution and order for a Gaussian PSF of 30% relative bandwidth.

Fig. 5

SNR versus resolution and order for a Gaussian PSF of 50% relative bandwidth.

Fig. 6

SNR versus resolution and order for a Gaussian PSF of 100% relative bandwidth.

Fig. 7

SNR versus resolution and order for a Gaussian PSF of 150% relative bandwidth.

Fig. 8

Example of an asymmetric echo function for $g$.

Fig. 9

SNR versus resolution and order for symmetrical and nonsymmetrical PSF.

Fig. 10

Cost function: the curve shows the loss function after extraction of the minima. As can be seen, the minimum is achieved for $m_0=2$.

Fig. 11

Comparison between synthetic original and processed images: (a) original 3 MHz image, (b) 6 MHz image, which is the ground truth, and (c) the processed image obtained from the original 3 MHz image, with our method.

Fig. 12

Comparison between profiles: profiles of the log-envelope of an extracted radio frequency line located in the top of Fig. 11 (solid line) from the synthetic 3 MHz image (solid), the synthetic 6 MHz image (dash dot), and processed images (dash).

Fig. 13

Comparison between the expected theoretical image (a), the original ultrasound image of a phantom consisting of a thread embedded in a gel (b), and the processed image (c) obtained from the original ultrasound image. The thread edge is sharper on the processed image.

Fig. 14

Comparison of visual appreciation of different methods on different images. From left to right, first column: the original images, second column: the results for homorphic filtering, third column: the results for HYPIF, and fourth column: the results of the proposed method. From top to bottom, first row: a mouse bladder image, second row: rabbit eye image, third row: uterus of a pregnant mouse, and fourth row: a synthetic image.